This is a multicenter, safety and pharmacokinetic trial to determine the MTD and/or select a recommended phase 2 dose (RP2D) of vemurafenib in children with recurrent or refractory gliomas containing the BRAFV600E or BRAF Ins T mutation. Using the RP2D, the study team will then conduct a Phase 0 study in a pre-surgical cohort of 10 patients requiring debulking surgery at the time of recurrence. These patients will receive neo-adjuvant vemurafenib, thus allowing the study team to measure intra-tumoral drug concentrations and target inhibition. An expansion cohort will then be enrolled to allow the study team to preliminarily estimate efficacy.